PaperlayerView exact revision on arXiv

Source-linked AI summary

Learning without neurons in physical systems

Menachem Stern, Arvind Murugan

arXiv:2206.05831v1cond-mat.dis-nncond-mat.softcond-mat.stat-mech

TL;DR

Physical learning addresses how physical systems can solve inverse problems by autonomously adapting without requiring computational design or an accurate system model. The review synthesizes theoretical and experimental work across materials and networks, showing how local rules and intrinsic dynamics support learning while physical constraints shape capabilities and signatures.

  • Problem

    Physical learning asks how systems can adopt desired behaviors and solve inverse problems without requiring computational design or an accurate model of the system.

  • Method

    The review synthesizes autonomous physical learning machines, their local learning rules, material implementations, constraints, and physical signatures across molecular, mechanical, and networked systems.

  • Results

    The reviewed systems demonstrate that physical learning can adapt material parameters and interactions, support functions such as self-assembly and pattern recognition, and produce distinctive physical signatures.

  • Takeaways & Limitations

    Physical learning offers a framework in which the same physical elements both perform functions and adapt those functions, motivating a theory of learning under physical constraints.

  • Takeaways & Limitations

    A principal difficulty is that the underlying physics must permit a useful local learning rule.

Abstract

from arXiv · show

Learning is traditionally studied in biological or computational systems. The power of learning frameworks in solving hard inverse-problems provides an appealing case for the development of `physical learning' in which physical systems adopt desirable properties on their own without computational design. It was recently realized that large classes of physical systems can physically learn through local learning rules, autonomously adapting their parameters in response to observed examples of use. We review recent work in the emerging field of physical learning, describing theoretical and experimental advances in areas ranging from molecular self-assembly to flow networks and mechanical materials. Physical learning machines provide multiple practical advantages over computer designed ones, in particular by not requiring an accurate model of the system, and their ability to autonomously adapt to changing needs over time. As theoretical constructs, physical learning machines afford a novel perspective on how physical constraints modify abstract learning theory.

1. INTRODUCTION

Physical learning applies bottom-up learning to physical materials, which autonomously modify their parameters from examples or stimuli rather than relying on centralized computational design. Its local rules exploit collective dynamics while imposing physical constraints that can also improve scalability and robustness.

  • 1.1. Physical learning: Inverse problems seek physical systems with desired responses, but their non-unique solutions make them harder than forward prediction and motivate learning-based design.Computational design varies system parameters through centralized, top-down approaches.
  • 1.1. Physical learning: Physical learning evaluates responses to training stimuli and incrementally modifies learning degrees of freedom until subsequent responses improve.The process separates evaluating output from modifying the system based on that output.
  • 1.1. Physical learning: Physical learning machines use physical degrees of freedom, learning degrees of freedom, and a system-dependent rule that updates parameters from the system’s response to stimuli.The framework includes unsupervised learning without supervisor intervention and supervised learning using an externally provided error signal.
  • 1.2. Why learn using a physical system?: Physical learning can use real examples without computer models, allowing materials to account for imperfections and potentially learn new behaviors in situ.The approach is especially suited to physical inputs and outputs such as forces, currents, and molecule production.
  • 1.3. Challenge and opportunity: local learning rules: Local rules update a parameter from nearby state information, while collective physical dynamics can encode distant system-wide information in that local state.Locality constrains learning but can support desynchronized, robust, and better-scaling systems without a central processor.
  • 1.4. Relationship to machine learning, neuromorphic computing and physical computation: Unlike physical computation and reservoir computing, physical learning machines autonomously learn what computation or behavior to perform by experiencing desired examples.Reservoir computing instead trains a computer-based output filter while leaving the physical reservoir unchanged.

2. EXAMPLES OF PHYSICAL LEARNING MACHINES

Physical learning has been demonstrated or modeled in mechanical, molecular, flow, neuromorphic, and other physical systems. These systems adapt material parameters or interactions through local or intrinsic processes to produce learned responses, pattern recognition, or transport behaviors.

  • 2.1. Mechanical systems: Elastic networks and creased sheets learn mechanical responses by modifying bond lengths, bond stiffnesses, or crease stiffnesses under imposed stimuli.Examples include learned auxetic responses and bifurcated folding pathways.
  • 2.2. Molecular systems and active matter: Molecular interactions can be learned through species creation or preferential multiplication, enabling concentration-dependent interactions and pattern recognition through self-assembly.A Hebbian-inspired rule strengthens interactions between species that are co-localized in space and time.
  • 2.2. Molecular systems and active matter: Molecular systems can also learn through growth, potentially storing multiple stable configurations, while molecular circuits use associative learning and intrinsic stochasticity.Hydrogels and DNA nanotubes grow elements based on current geometry; crystals with defects may show rudimentary evolution through fracture and growth.
  • 2.2. Molecular systems and active matter: Autonomous learning at the molecular scale remains undemonstrated for active matter, although simulations and macroscopic robotic swarms suggest related possibilities.Proposed mechanisms combine synthetic active matter with DNA elements or rearrange nematic or polar filaments.
  • 2.3. Flow networks: Flow networks can adapt pipe properties through local feedback, supporting learned transport behaviors and theoretical classification of stimuli without a central controller.Examples span biological networks such as vasculature and engineered microfluidic systems.
  • 2.4. Neuromorphic and related systems: Neuromorphic systems adapt electronic or optical elements and increasingly use local contrastive-learning rules for regression and classification, whereas deep physical networks train physical parameters with backpropagation.These approaches seek machine-learning performance in energy and robustness while exploiting physical dynamics.

3. PHYSICAL LEARNING RULES

Physical learning rules let materials modify local parameters in response to stimuli, spanning unsupervised adaptation and supervised training toward specified responses.

  • Unsupervised learning: Unsupervised physical learning changes material parameters directly from observed responses, without supervisor intervention.The learning rule updates degrees of freedom according to the system’s stimulus-dependent state.
  • Unsupervised learning: Local aging rules can train elastic networks toward desired states by reducing their energy through stress-dependent bond changes.Because network energy sums over bonds, each bond can update according to the stress or energy it carries.
  • Unsupervised learning: Molecular Hebbian learning strengthens or weakens interactions when molecular species are spatially and temporally proximate, enabling multiple self-assembly behaviors and pattern recognition.Proximity-based ligation creates interaction-mediating molecules, while related mechanisms include strand displacement and phosphorylation.
  • Unsupervised learning: Flow networks can adapt through unsupervised rules based only on local edge flow or pressure differences.These rules change network properties according to flow through edges, proportional to pressure drops between nodes.
  • Supervised learning: Supervised physical learning uses feedback about correct or incorrect responses to minimize a cost over labeled stimulus classes.Thumbs-up/thumbs-down rules switch the sign of local adaptation, while contrastive learning compares current and nudged improved responses and can approximate global-cost gradients.
  • Supervised learning: A creased sheet learned to classify force patterns from Iris data by developing a heterogeneous crease-stiffness profile through local adaptation.Contrastive rules were also shown to yield local, physically realizable learning rules and to train several physical models in silico.

4. CHALLENGES IN IMPLEMENTING PHYSICAL LEARNING

Implementing physical learning requires suitable local physics, controllable material parameters, and strategies for supervision, locality, noise, and finite adaptability.

  • 4.1. Physical implementation of supervision: The principal implementation difficulty is finding underlying physics that supports a useful local learning rule.This requirement constrains which physical substrates can realize learning machines.
  • 4.1. Physical implementation of supervision: Supervised learning requires materials to strengthen or weaken interactions according to contextual feedback, while contrastive rules additionally require duplicated or sequentially reused system states.These demands make supervised and especially contrastive implementations more physically challenging than unsupervised rules.
  • 4.2. Locality in solid and liquid-like systems: Liquid-like systems with few species remain challenging because they lack fixed neighbors, so broader learning protocols must exploit changing geometric arrangements.This boundary affects jammed sphere packings and actin or microtubule networks.
  • 4.3. Exploiting noise: Physical noise perturbs both stimulus responses and parameter updates, but distributed asynchronous learning can tolerate damaged elements and may benefit tasks requiring randomness.Noise has been associated with stochastic learning, robust memories, and possible generalization benefits; physical rules can remain robust with an error floor.
  • 4.4. Material constraints: dynamic range of weights w, over-training: Real materials limit the dynamic range of learning degrees of freedom, although material choice and larger architectures can partly compensate.Examples include finite molecular interaction ranges and bounded mechanical stiffnesses; larger networks can distribute required changes across more elements.
  • 4.4. Material constraints: dynamic range of weights w, over-training: Positive-only parameters and overtraining further constrain learning, because exhausted variability can prevent adaptation to new tasks.Proposed physical analogs include shifting positive interactions or representing signed weights through differences of positive weights.

5. PHYSICAL MANIFESTATIONS OF LEARNING CONCEPTS

Physical learning connects memory, timescale, equilibrium, architecture, and expressivity to how materials acquire and reproduce desired behaviors. These systems can learn despite overlapping response and learning timescales, while noise, nonequilibrium dynamics, topology, and hidden degrees of freedom shape their capabilities.

  • 5.1. Memory, learning and generalization: Learning requires selective, functional memory with a physical retrieval mechanism, enabling appropriate responses to familiar and novel stimuli rather than overfitting.Memory stores past stimuli, but generalization requires retaining informative features instead of every training detail.
  • 5.2. Learning out of equilibrium: Learning can succeed when τlearn ∼τresponse, although sufficiently high learning rates may produce oscillations.Physical systems need not cleanly separate stimulus-response dynamics from learning dynamics, unlike typical in silico training.
  • 5.2. Learning out of equilibrium: Non-equilibrium nucleation can improve molecular pattern-recognition capacity while trading off recognition complexity, accuracy, and speed.Non-reciprocal interactions are also proposed to expand the range of learnable behaviors.
  • 5.4. Dynamic architectures, continual learning and forgetting: Physical learning can alter topology and architecture, allowing growth, self-assembly, or molecular interactions to construct task-compatible networks.This architectural freedom differs from systems whose learning primarily updates weights within a fixed structure.
  • 5.4. Dynamic architectures, continual learning and forgetting: Natural forgetting through degradation can let physical systems learn new tasks without exceeding capacity set by their number of degrees of freedom.Erasure and forgetting therefore support continual adaptation rather than permanent accumulation of learned experiences.
  • 5.5. Expressivity, capacity, and hidden nodes: Expressivity and capacity increase with physical learning degrees of freedom, while frustrated interactions, dimensionality, and hidden nodes can support more complex behaviors.Broad principles governing which physical interactions increase expressivity remain unavailable.
  • 5.6. Physical signatures of learning: Trained physical systems develop substrate signatures including heterogeneity, changed connectivity, soft modes, reduced response dimension, and performance-energy trade-offs.These signatures can arise beyond the functionality explicitly targeted during learning.

6. PHYSICAL SIGNATURES OF PAST LEARNING

Past learning leaves physical systems in atypical, task-relevant states rather than generic disordered configurations. Its signatures include heterogeneous architectures, adaptive networks, non-glassy energy landscapes, and soft modes that reorganize responses and energetic demands.

  • 6.1. Network geometry and topology: Learning produces spatial and interaction heterogeneity, including varied elastic moduli, tube radii, pruned edges, and atypical molecular interaction patterns.These structures can be unlike the random ensembles commonly used to study disordered systems.
  • 6.1. Network geometry and topology: Alternating incompatible tasks can discover mutable networks that switch behaviors with fewer parameter changes than generic designed networks.Such systems are described as rare but highly adaptive networks.
  • 6.2. Network dynamics: Learning creates non-glassy landscapes with exponentially fewer, non-random minima, including chimeric assemblies near capacity and fewer bifurcation branches in trained sheets.Jammed packings can likewise become ultra-stable through aging in a selected state.
  • 6.2. Network dynamics: Trained systems often develop soft modes that concentrate responses along low-dimensional directions and can reduce the energy required to actuate desired behaviors.Soft modes may appear even when softness was not an explicit training objective.

7. CONCLUSION

The review frames autonomous physical learning as a distinct approach shaped by physical constraints, with implications for understanding learning as a physical and collective phenomenon.

  • 7. CONCLUSION: Physical learning is presented as distinct from neuroscience and machine learning because physical machines can solve inverse problems and produce responses without biological or computational analogies.The review emphasizes that this distinctiveness arises from treating learning as a physical phenomenon.
  • 7. CONCLUSION: The review identifies physical constraints as central to autonomous learning machines and discusses ways some of those constraints can be overcome.
  • 7. CONCLUSION: Treating learning physically motivates fundamental questions about realizable models, collective behavior in simple systems, and learning-induced physical changes.The authors suggest these questions may support a fundamental physical theory of learning independent of implementation details.
  • 7. CONCLUSION: Progress in physical learning requires multidisciplinary theoretical and experimental research involving condensed matter physics, computer science, and neuroscience.

DISCLOSURE STATEMENT

The authors report no known affiliations, memberships, funding, or financial holdings that might affect the review’s objectivity.

  • DISCLOSURE STATEMENT: The authors report no affiliations known to affect the review’s objectivity.
  • DISCLOSURE STATEMENT: The authors report no memberships known to affect the review’s objectivity.
  • DISCLOSURE STATEMENT: The authors report no funding or financial holdings known to affect the review’s objectivity.
Loading 2206.05831v1…